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With the increasing importance of deep learning workloads, many hardware accelerators have been proposed in both academia and industry. However, software tooling for the vast majority of them does not exist compared to the software ecosystem and innovations proposed for established platforms such as CPUs and GPUs. We observed that the lack of well-de!ned hardware-software interfaces and correctness testing tools like fast and scalable test oracles (also known as functional simulators) act as significant barriers to adopting these emerging accelerators in the software community. These interfaces and tools are essential in building software such as retargetable compilers and optimized kernels. To bridge these gaps, we first present TAIDL, an instruction specification language that provides novel constructs to describe the instruction set architectures (ISAs) of tensor accelerators. Next, given ISA definitions in TAIDL, we introduce techniques to automatically generate fast and scalable test oracles for diverse sets of accelerators, which are needed for testing software correctness of code that targets pre-silicon hardware designs. Automated generation of such tools reduces the burden on hardware architects and the repeated development efforts required across different accelerator platforms. Further, our techniques allow us to execute these simulators on GPUs, leading to highly scalable simulations. To demonstrate the expressivity of TAIDL, we instantiated several tensor accelerator ISAs with different compute capabilities and memory hierarchies. Further, we show that test oracles generated using TAIDL definitions are orders of magnitude faster and more scalable than existing instruction-level functional simulators, making them suitable for integration into software development cycles. TAIDL is available at https://github.com/act-compiler/taidl. 

Tensor compilers, essential for generating efficient code for deep learning models across various applications, employ tensor graph rewrites as one of the key optimizations. These rewrites optimize tensor computational graphs with the expectation of preserving semantics for tensors of arbitrary rank and size. Despite this expectation, to the best of our knowledge, there does not exist a fully automated verification system to prove the soundness of these rewrites for tensors of arbitrary rank and size. Previous works, while successful in verifying rewrites with tensors of concrete rank, do not provide guarantees in the unbounded setting. To fill this gap, we introduce TensorRight, the first automatic verification system that can verify tensor graph rewrites for input tensors of arbitrary rank and size. We introduce a core language, TensorRight DSL, to represent rewrite rules using a novel axis definition, called aggregated-axis, which allows us to reason about an unbounded number of axes. We achieve unbounded verification by proving that there exists a bound on tensor ranks, under which bounded verification of all instances implies the correctness of the rewrite rule in the unbounded setting. We derive an algorithm to compute this rank using the denotational semantics of TensorRight DSL. TensorRight employs this algorithm to generate a finite number of bounded-verification proof obligations, which are then dispatched to an SMT solver using symbolic execution to automatically verify the correctness of the rewrite rules. We evaluate TensorRight’s verification capabilities by implementing rewrite rules present in XLA’s algebraic simplifier. The results demonstrate that TensorRight can prove the correctness of 115 out of 175 rules in their full generality, while the closest automatic, bounded-verification system can express only 18 of these rules. 

Tensor compilers, essential for generating efficient code for deep learning models across various applications, employ tensor graph rewrites as one of the key optimizations. These rewrites optimize tensor computational graphs with the expectation of preserving semantics for tensors of arbitrary rank and size. Despite this expectation, to the best of our knowledge, there does not exist a fully automated verification system to prove the soundness of these rewrites for tensors of arbitrary rank and size. Previous works, while successful in verifying rewrites with tensors of concrete rank, do not provide guarantees in the unbounded setting. To fill this gap, we introduce TensorRight, the first automatic verification system that can verify tensor graph rewrites for input tensors of arbitrary rank and size. We introduce a core language, TensorRight DSL, to represent rewrite rules using a novel axis definition, calledaggregated-axis, which allows us to reason about an unbounded number of axes. We achieve unbounded verification by proving that there exists a bound on tensor ranks, under which bounded verification of all instances implies the correctness of the rewrite rule in the unbounded setting. We derive an algorithm to compute this rank using the denotational semantics of TensorRight DSL. TensorRight employs this algorithm to generate a finite number of bounded-verification proof obligations, which are then dispatched to an SMT solver using symbolic execution to automatically verify the correctness of the rewrite rules. We evaluate TensorRight’s verification capabilities by implementing rewrite rules present in XLA’s algebraic simplifier. The results demonstrate that TensorRight can prove the correctness of 115 out of 175 rules in their full generality, while the closest automatic,bounded-verification system can express only 18 of these rules.